Effective Multi-level Monte Carlo Methods for Stochastic Biochemical Kinetics

Stochastic mathematical models are essential for an accurate description of biochemical processes at the cellular level. The effect of random fluctuations may be significant when some species have low molecular counts. While exact stochastic simulation methods exist, they are typically expensive on systems arising in applications. Thus more effective strategies are required for simulating complex stochastic models of biochemical system. Often, the expected value of some function of the final time solution of the stochastic model is of interest. Then, the approach employing multi-level Monte Carlo methods is more efficient than the traditional techniques. In this thesis, we study multi-level Monte Carlo (MLMC) schemes for a reliable and effective simulation of stochastic models of biochemical kinetics. The advantages of these MLMC strategies are illustrated on several biochemical models arising in applications.

Effective Multi-level Monte Carlo Methods for Stochastic Biochemical Kinetics

Stochastic mathematical models are essential for an accurate description of biochemical processes at the cellular level. The effect of random fluctuations may be significant when some species have low molecular counts. While exact stochastic simulation methods exist, they are typically expensive on systems arising in applications. Thus more effective strategies are required for simulating complex stochastic models of biochemical system. Often, the expected value of some function of the final time solution of the stochastic model is of interest. Then, the approach employing multi-level Monte Carlo methods is more efficient than the traditional techniques. In this thesis, we study multi-level Monte Carlo (MLMC) schemes for a reliable and effective simulation of stochastic models of biochemical kinetics. The advantages of these MLMC strategies are illustrated on several biochemical models arising in applications.

An Efficient Tau-Leaping Simulation Method for Stochastic Biochemical Kinetics

Stochastic modeling and simulation of biochemical systems are topics of high interest in Computational Biology. Stochastic mathematical models are critical in accurately capturing the variability observed experimentally in cellular processes, in particular when some species have low molecular numbers. Many, realistic biochemical networks exhibit stiffness, due to the presence of multiple time-scales. For such networks explicit simulation methods are computationally quite intensive. In this thesis, we introduce an improved implicit tau-leaping strategy for the simulation of stochastic biochemical kinetic models. Numerical tests on various biochemical systems of interest in applications show the efficiency of our method.

An Efficient Tau-Leaping Simulation Method for Stochastic Biochemical Kinetics

Stochastic modeling and simulation of biochemical systems are topics of high interest in Computational Biology. Stochastic mathematical models are critical in accurately capturing the variability observed experimentally in cellular processes, in particular when some species have low molecular numbers. Many, realistic biochemical networks exhibit stiffness, due to the presence of multiple time-scales. For such networks explicit simulation methods are computationally quite intensive. In this thesis, we introduce an improved implicit tau-leaping strategy for the simulation of stochastic biochemical kinetic models. Numerical tests on various biochemical systems of interest in applications show the efficiency of our method.

Spatial and temporal studies of metabolic activity: contrasting biochemical kinetics in tissues and pathways during fasted and fed states

The regulation of nutrient homeostasis, i.e., the ability to transition between fasted and fed states, is fundamental in maintaining health. Since food is typically consumed over limited (anabolic) periods, dietary components must be processed and stored to counterbalance the catabolic stress that occurs between meals. Herein, we contrast tissue- and pathway-specific metabolic activity in fasted and fed states. We demonstrate that knowledge of biochemical kinetics that is obtained from opposite ends of the energetic spectrum can allow mechanism-based differentiation of healthy and disease phenotypes. Rat models of type 1 and type 2 diabetes serve as case studies for probing spatial and temporal patterns of metabolic activity via [2H]water labeling. Experimental designs that capture integrative whole body metabolism, including meal-induced substrate partitioning, can support an array of research surrounding metabolic disease; the relative simplicity of the approach that is discussed here should enable routine applications in preclinical models.

Computational Modeling of Coagulopathy for Decision Support

Nearly everyone, throughout their life, is at risk of being involved in a serious traumatic event, such as motor vehicle accidents, sports and occupational injuries, or natural disaster related injuries. Twenty-eight percent of trauma patients precipitously develop abnormalities in their blood coagulation system. These coagulopathies increase their mortality rate by 5fold. The current coagulopathy diagnosis protocol collects basic patient information, vital signs, and performs traditional lab and point-of-care (POC) blood testing. A high-stakes decision must then be made by the trauma surgeon, using their intuition, training, and the results from the blood drawn at least 15 minutes prior, to determine the requirement for a resuscitation treatment through coagulation inhibitors or activators. Computational modeling and system analysis of the human blood coagulation are integral to developing superior decision support tools for trauma surgeons. In short, the coagulation system consists of the following functional subsystems: 1) blood flow, 2) platelet function, 3) diffusion, 4) advection, and 5) biochemical kinetics. We utilize a combined approach of both 0-D and 3-D model development with the overarching goal of developing a validated, near real-time decision support system. The biochemical kinetics of the coagulation system is implemented in the 0-D model with a set of 113 nonlinear, coupled ordinary differential equations (ODEs), describing the time rate of change of the numerous chemical concentrations and their interaction with one another. 0-D models provide a fast, efficient means of simulating the coagulation biochemical kinetics, but these ODEs lack the ability to describe the global effects of fluid flow, advection, and diffusion. Hence, the set of 113 ODEs are modeled as source terms and combined with the Navier-Stokes and chemical advection/diffusion equations in a three-dimensional finite volume computational domain, providing a global coagulation model. Model validation studies employ parallel experimental POC blood testing and 3-D computational modeling. Results from the 0-D model are consistent with testimonials from expert trauma surgeons, whom verify the model provides appropriate reasoning for their difficulties in predicting patient outcome. Thus, validated computational models have potential as a hypothesis generator used for developing new approaches for providing trauma surgeons with sufficient information to make better informed clinical decisions, “the decision support tool,” leading to decreased mortality.